Johnny and his sister Jane race up a hill.Johnny weights twice as much as jane and takes twice as long as jane to reach the top.Compared to jane

Options

A. Johnny did more work and delivered more power
B. johnny did more work and delivered the same amount of power
C. Johnny did more work and delivered less power
D. Johnny did less work and johnny delivered less power

Explanation

To solve the problem step by step, we need to analyze the situation involving Johnny and Jane racing up a hill.

### Step 1: Define the weights and times
Let:
- Jane's weight = \( mg \) (where \( m \) is Jane's mass and \( g \) is the acceleration due to gravity)
- Johnny's weight = \( 2mg \) (since Johnny weighs twice as much as Jane)
- Let Jane's time to reach the top = \( t \)
- Therefore, Johnny's time to reach the top = \( 2t \) (since Johnny takes twice as long as Jane)

### Step 2: Calculate the work done by each
The work done against gravity to reach the height \( h \) is given by the formula:
\[ \text{Work} = \text{Weight} \times \text{Height} \]

For Jane:
- Work done by Jane = \( mg \cdot h \)

For Johnny:
- Work done by Johnny = \( 2mg \cdot h \)

### Step 3: Calculate the power for each
Power is defined as the work done per unit time.

For Jane:
\[ \text{Power}_{\text{Jane}} = \frac{\text{Work done by Jane}}{\text{Time taken by Jane}} = \frac{mg \cdot h}{t} \]

For Johnny:
\[ \text{Power}_{\text{Johnny}} = \frac{\text{Work done by Johnny}}{\text{Time taken by Johnny}} = \frac{2mg \cdot h}{2t} = \frac{mg \cdot h}{t} \]

### Step 4: Compare the powers
From the calculations:
- Power of Jane = \( \frac{mg \cdot h}{t} \)
- Power of Johnny = \( \frac{mg \cdot h}{t} \)

### Conclusion
Both Johnny and Jane deliver the same amount of power while racing up the hill.